Rovers' gloom was completed by the 70th-minute dismissal of their top scorer, Jason Roberts, who lashed out at Neil Smith as the players waited for a free-kick to be taken.
Fulham now lead the table by 12 points from Preston, having played a game more.
The game was played in atrocious conditions as torrential rain left puddles all over the pitch.
First-half goals from Kit Symons and Geoff Horsfield put Kevin Keegan's Fulham in command, but Andy Thomson pulled a goal back in first-half injury time.
Fulham had defended the better but paid the penalty for leaving Thomson unmarked at Ian Holloway's corner.
That gave Rovers renewed hope and Roberts skated between two defenders to put them level before Trollope timed his run perfectly to meet a Steve Finnan cross to send the travelling fans home happy.
Symons had put Fulham ahead with a close-range shot after nine minutes and Horsfield capitalised on a mistake by Robbie Pethick to snatch the second.
Bristol Rovers: Jones, Pethick, Challis, Trees (Ellington 73), Thomson (Trought 62), Foster, Shore, Hillier, Holloway, Cureton, Roberts. Substitute not used: Johnson. Fulham: Taylor, Finnan, Brevett, Morgan, Coleman, Symons, Hayward, Smith, Horsfield, Trollope, Hayles (Peschisolido 83). Substitutes not used: Uhlenbeek, Betsy.
Referee: P Robinson (Hull).